The invention relates to sensing and control of polarization in optical beams using feedback, and to optical telecommunication systems where control of polarization and of polarization mode dispersion are important.
It is routine to measure polarization by means of serial measurements of intensity while a polarization sensitive element such as a waveplate or polarizer is mechanically rotated, or engaged and disengaged from the beam. Electro-optic approaches are used, where variable retarders such as pockels cells, Kerr cells, liquid crystal cells, optical rotators, and the like are driven to different settings while the beam is analyzed at a fixed polarizer or other element. The mechanical systems are unwieldy, and the electro-optic systems are costly; both are inherently slow and vulnerable to time-fluctuations in the beam being measured since they employ serial measurements of intensity.
Other approaches are possible, such as the use of two detectors at the outputs of a Wollaston prism. This is rugged and provides rapid information about the state of polarization (SOP) of a beam, but the information is incomplete, being typically limited to at most two of the four Stokes parameters. The cost of a Wollaston prism or similar displacing element is considerable, another problem with this approach.
Azzam teaches in U.S. Pat. No. 4,681,450 an apparatus for sensing polarization of a monochromatic beam, based on several photodiodes in a three-dimensional configuration that reflects light from a first detector onto a second detector and finally onto a third. The reflections are at significantly non-normal incidence, and the detectors have polarization-dependent reflection coefficients, which enable calculation of the incident SOP from the three detector readings. The apparatus is dependent on the surface properties of the detectors, and often requires calibration of each instrument. Further, it is only suitable for use over a limited range of wavelengths, since the reflection coefficients are wavelength-dependent. Finally, the configuration of several detectors is awkward to construct and costly to package, compared to simple mounting of detectors on a printed-circuit board or the like. These factors all vitiate against low cost in a mass-production fashion. The alternative arrangement of Azzam in U.S. Pat. No. 4,725,145 requires fewer photodetectors (only one or two, rather than four) but they must be mechanically rotated to derive the state of polarization.
In short, all prior-art method for sensing SOP suffer one or more of the following limitations: high cost, slow speed, mechanical moving parts, incomplete information about the SOP, need for calibration, critical dependence on detector reflection properties, and inability to sense SOP for a polychromatic beam. There is at present no rugged and economical means for sensing complete SOP information.
Turning to polarization control, Clark teaches a polarization controller in U.S. Pat. No. 5,005,952, based on a stack of multiple liquid crystal variable-retarder cells controlled by means of a feedback signal. He further teaches means for transforming a continuously varying SOP to a fixed linear state by use of four such cells, or by a pair of three-cell stacks with switching means to direct the incident beam to one or another of the stacks.
Rumbaugh et. al. teach a polarization controller in U.S. Pat. No. 4,979,235, based on a stack of three liquid crystal variable-retarder cells. He further discloses a method for generating a continuously-varying SOP from a fixed linear SOP using only a single three-cell stack with no switching means. The method is based on optimizing the output of a homodyne detector by noting the change in output while the drive signal is adjusted in a certain sense for each of two liquid crystal cells, one after the other. The detector output is monitored after each adjustment, and the sense of adjustment is reversed in subsequent loop iterations for a given cell if the previous adjustment decreased the detector output. Thus, if the first adjustment to a given cell has the wrong sense to produce the desired SOP, a total of four adjustments are requiredxe2x80x94two adjustments to each of the two cellsxe2x80x94before the feedback begins to be beneficial.
This complicated and unwieldy control method is inherent in such a system where there is only one feedback signal from which adjustment of two cells must be derived. And, since the signal attains a local maximum at the desired operating point, the feedback sense changes from negative (stable) to positive (unstable) when the controller passes through the optimum response. An equivalent situation occurs if the signal attains a local minimum at the desired operating point. Overall, the servo action is not deterministic, but works by trial-and-error xe2x80x98huntingxe2x80x99: it hunts to determine which retarder needs adjustment, and it hunts to determine whether an increase or decrease in retardance is needed.
Miller teaches feedback control of a liquid crystal variable retarder in U.S. Pat. No. 4,848,877, based on an optical signal passing through the retarder.
Various prior-art references describe the use of mechanical means to adjust the SOP of light in an optical fiber by squeezing the fiber. Firms supplying such equipment commercially include Oz Optics (Carp, Ontario, Canada), FiberPro (Taejon, Korea), and Optics For Research (Caldwell, N.J.).
Systems for SOP compensation and control of have been proposed based on the optoceramic materials sold by NZ Applied Technologies (Woburn, Mass.).
Dithering systems of various kinds are known for maximizing signals which have a periodic sinusoidal (or similar) dependence on a control variable. Some dither the control at a frequency Fd which is faster than the servo response of the system Fs, and look for a minimum in the envelope of response at Fd, which indicates that the flat top of the periodic response has been attained; or, they monitor the envelope of response at frequency 2Fd and seek a maximum, or combinations of these themes and variations upon them. However, these methods cannot be exploited when the control element has inherently slow time response and cannot be dithered at or above the servo response frequency.
Thus while various methods have been shown for polarization control, or for control of liquid crystal variable retarders, none provides for deterministic servo control that is free from hunting, nor that produces a stable output with rapid time response to changes in the input SOP, and that exhibits low output error. It is the aim of the present invention to provide these capabilities. It is further an aim to provide this in a controller with only three variable retarder stages, which nonetheless has the capacity to transform a continuously-variable SOP to a desired state. It is yet a further aim of this invention to provide a control action that is robust in the face of intensity changes in the incident beam, and to achieve a high optical efficiency or throughput.
The invention consists of an apparatus that samples the SOP of a beam, that may optionally be placed in series with a polarization compensator to sample the SOP of the compensated beam. The compensator may be built using any type of control element, including liquid crystal cells, fiber optic squeezers, opto-ceramic modulators, lithium niobate modulators, or any other device which acts as a polarization compensator. In a preferred embodiment, the compensator comprises three retarders that transform incident light with a Ad continuously-varying SOP to be linearly polarized along a specified polarization axis. The first and third variable retarder have their fast or slow axes oriented at 45xc2x0 to the exit polarization axis, to which either the fast or slow axis of the middle variable retarder is parallel. The middle variable retarder may be constructed as two liquid crystal cells with parallel (or perpendicular) slow axes, so they act in concert as a single retarder whose retardance is the sum (or difference) of their individual retardances.
The SOP sampling apparatus uses retarders and polarization-sensitive beamsplitters that direct light towards two or three photodetectors. The detectors may be operated at normal incidence, and need not have any special polarization sensitivity in their response. Often, the desired SOP is a linearly polarized state, which is represented by a point on the equator of the Poincare sphere; we define the co-ordinate system of the sphere so this location has a longitude of 0xc2x0 and corresponds to horizontally polarized light. The SOP may be sampled by assembling in series the following elements: a quarter wave plate with its axis at 45xc2x0, a beamsplitter, a half-wave plate with its axis at 22.5xc2x0, a second beamsplitter, and a quarter-wave plate with its axis at 45xc2x0.
The beamsplitters produce sample beams whose intensities indicate the Poincare latitude and longitude, respectively, of the SOP produced by the polarization controller. These signals preferably are orthogonal in the sense that a change in latitude does not alter the longitude signal, and vice versa. They are preferably monotonic functions of latitude or longitude for output SOPs near the desired SOP. The ability to sense not only the presence of a deviation from a desired SOP, but the magnitude and vector direction of the deviation, is of great benefit in polarization control and in systems for control of polarization mode dispersion.
When the SOP sensor is used together with a polarization compensator, the latter apparatus is preferably designed so that one variable retarder adjusts the Poincare latitude, and another variable retarder adjusts Poincare longitude, or an equivalent arrangement. The action of the retarders is thus orthogonal and there is a one-to-one correspondence between a specific parameter measured by the SOP sensor, and a control element in the polarization compensator which adjusts that specific parameter. Errors in the sensed longitude may be corrected by adjusting the compensator element that adjusts longitude, and similarly for latitude. Servo control of the SOP is readily achieved by the use of independent control circuitry for each of these parameters. Further, since the beamsplitter signals can be made monotonic in the neighborhood of the desired SOP, there is no sign ambiguity in the sense of feedback, so there is no hunting.
It is possible to achieve a small-signal servo gain-bandwidth of several hundred Hz or more using liquid crystal variable retarders to control light at 1.55xcexc. This is at least 10xc3x97 faster than is achieved using the method of Rumbaugh with the same liquid crystal retarders. The increase is due to five factors. First is the use of two beamsplitter signals keyed to which retarder needs adjustment. This provides a speed advantage over prior-art systems, which have only a single signal and must try adjusting two retarders in time-sequence to determine which one actually needed adjustment.
Second, the fact that these signals vary in a monotonic fashion provides a speed advantage over prior-art systems which provided a control signal having a local maximum or minimum at the desired SOP. In prior-art systems the function describing signal intensity versus retarder setting changes sign at the desired SOP, so the feedback sense constantly changes from negative (stable) to positive (runaway error) during operation. Control errors are frequent, and the system response must be tested after every adjustment, to see whether or not the feedback sense has changed since the last adjustment. The provision of signals that vary in a monotonic fashion with output SOP eliminates these control errors and eliminates the need for testing for feedback sense after each adjustment.
Third, the present system provides a signal that is linear for modest excursions in SOP. In contrast, prior art systems tend to seek an extremum such as a signal maximum or minimum. In the vicinity of the desired SOP, the slope of the response curve is actually zero. Small excursions produce a disproportionately small signal from the SOP sensor, making it very difficult to produce a system with low SOP error. In contrast, the present invention produces a signal that is linear with SOP excursion in the neighborhood of the desired SOP. Construction of low-error systems is greatly facilitated as a result. Further, the nonlinear prior-art systems degrade the speed of response when used in a servo system, since the effective gain of the system varies with the sensitivity of the SOP sensor.
Fourth, servo control in the present invention can be continuous in time, rather than discrete in time. Prior-art systems required discrete-time control in order to isolate which retarder needed adjustment, and in what sense. Sufficient time had to be provided after each adjustment so that the effect of previous adjustments was substantially complete, and did not confound the determination at hand.
Fifth, prior-art systems using discrete time control needed to operate at relatively slow sample rates. While modern control and state-space control theory provide for discrete-time control at sample rates exceeding twice the natural response frequency of the system being controlled, liquid crystal retarders do not meet the criteria for using such techniques. In addition to being nonlinear in response, their time-response is different (by up to 10xc3x97) for increases in drive level versus decreases in drive level. This effect is most pronounced for large excursions, which in turn are most prevalent when there is large servo error due to servo hunting. In practice, prior-art systems we built could only be successfully operated at the slower of the two rates (increases vs. decreases in drive).
The present invention eliminates this speed penalty, along with the need for discrete-time control, and the need to adjust two retarders in time-sequence, and the need to try adjustments in both senses to correct an error in output SOP, and the need to allow for the nonlinear response of the SOP sensor, and thereby achieves an overall speed gain of 10xc3x97 or more compared with the prior art.
The various features of novelty which characterize the invention are pointed out with particularity in the claims annexed to and forming a part of the disclosure. For a better understanding of the invention, its operating advantages, and specific objects attained by its use, reference should be had to the drawing and descriptive matter in which there are illustrated and described preferred embodiments of the invention.